100 lines
3 KiB
TeX
100 lines
3 KiB
TeX
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pdftitle={F25MB6\_Notes\_Greene\_Isaac},
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pdfauthor={Isaac Greene},
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\begin{document}
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\part*{MTH122:13 Notes}
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These notes have been digitally typeset and reassembled from scratch notes.
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\tableofcontents
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\section{2025-09-03}
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Notes on domain and range\footnote{Dr. Filiz Dogru was our sub on Friday (Sep 5) because Mrs. Brott was out. She has been a math professor at GV for over 23 years.}
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Find domain and range. Domain is x-axis, and range is y-axis.
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y-intercept = $f(0)$ or $(0, c)$
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x-intercept = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=0$
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Direction (end behavior) = if a > 0, as $x \longrightarrow \infty$, graph goes up.
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Axis of symmetry and $x_{vertex} = \frac{-b}{2a}$ in standard form but simply "h" in vertex form.
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$y_{vertex} = f(x)$ where $x = \frac{-b}{2a}$
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\begin{equation}
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f(x) = 2x^{2}-x-1
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\end{equation}
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\begin{equation}
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f(x) = \frac{1}{2*2} = \frac{1}{4} = 0.25
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\end{equation}
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\begin{equation}
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Vertex = (0.25, -1.125)
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\end{equation}
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\begin{equation}
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\frac{+1\pm\sqrt{-1^{2}-4(2)(-1)}}{2(2)}
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\end{equation}
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\begin{equation}
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\frac{1\pm\sqrt{1+8}}{4}
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\end{equation}
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\begin{equation}
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\frac{1\pm\sqrt{9}}{4} = \frac{1\pm3}{4} = \frac{-2}{4} and \frac{4}{4}\ so\ x=\{-0.5, 1\}
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\end{equation}
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\section{2025-09-10}
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\begin{equation}(x+2)(x+3)=0\end{equation} $\\6x^{2}+x-1=0\\
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x^{2}+5x+6x=0$
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\hrule
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$5x^{2}-7x+2=0$
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\begin{enumerate}
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\item When $a \neq 1$, multiply first and last term, ($5x^{2}\cdot2=10x$)
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\item Find two numbers that multiply to (first * last) and add to the middle term
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\item Replace middle term with the found numbers
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\item Split the polynomial in half, like $5x^{2}-5x-2x+2$ becomes $(5x^{2}-5x) | (-2x+2)$
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\item Factor each group
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\end{enumerate}
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$\frac{(5x^{2}}{5x}-\frac{5x)}{5x}$
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\end{document}
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